Line baking sheets with parchment paper or silicone baking mats and set aside. Sift flour, cornstarch, baking powder, baking soda, and salt.
In a stand mixer fitted with the paddle attachment beat 1/2 cup butter, sugar, and vanilla until fluffy. Add egg yolks one at a time until fully incorporated.
Add flour to wet mixture in stand mixer bowl while beating on medium-low speed. Slowly add in coconut shavings until incorporated. If dough appears dry, add heavy whipping cream 1 tablespoon at a time until dough is soft. Divide into two pieces, cover and chill for 1 hour.
Preheat oven to 325F. While dough is chilling, make the filling. Using the whisk attachment on a stand mixer with a clean bowl whip remaining butter, dulce de leche and 2 tablespoons cream on medium-low speed.
Once cream is fluffy, add food coloring one drop at a time until desired blue is achieved. Chill until ready to use.
Working with one piece of dough at a time, roll to 1/4-inch thick on a well floured surface. Using a 2 1/2-inch circular cookie cutter, cut rounds and transfer to baking sheets. Repeat with remaining dough.
Bake cookies for 15 minutes. Transfer cookies to cooling rack and cool completely.
While cooling, in small bowl combine coconut shavings with 1 to 2 drops of blue food coloring. Mix until desired coloring is achieved.
Pair each cookie with another that is a similar shape and size. Add 1 tablespoon filling to the flat side of each cookie, then sandwich together. Press cookies together until cream begins to pillow out of the sides. Roll sides in blue coconut shavings. Smear a bit of cream on top of cookies and dip in coconut shavings.